The "Your comment is awaiting moderation" message is created as follows:
<?php if ( $comment->comment_approved == '0' ) : ?> <em>Your comment is awaiting moderation.</em> <?php endif; ?>
If the "Comment author must fill out name and e-mail" option is checked in Discussion Settings, then the commenter will see his own comment, as well as "awaiting moderation" message after submitting.
If said option is unchecked (thus allowing anonymous comments), and the visitor does not enter a name, he won't see his comment, nor the message after submitting.
I tried this with a clean install and Twenty Twelve theme just to be sure.